A (directed) graph G=(V, E) consists of a set V of nodes
and a set E of ordered pairs of nodes.
An element 
is called an edge of the graph.
A graph is undirected if for each edge
also 
holds.
The set 
is the set of predecessors of a node 
.
The set 
is the set of all successors of a node v.
The sizes of these sets are
and 
.
The degree of a node v is 
.
A sequence 
is a path from 
to 
if there are edges 
for 
.
A cycle is a nonempty path from v to v.
A graph without cycles is called acyclic.
A graph is dense if it contains many edges and sparse if it
contains only few edges.
It would be superfluously pedantic to define these notions
precisely.
A graph with 
is always considered
sparse,
while a graph with 
is always considered
dense.
%